A key goal of evolutionary biology and human genetics is to understand how natural selection has shaped genetic and phenotypic variation within and among populations. The vast amount of population genomic data and genotype-phenotype mapping data generated over the coming decade will bring an unprecedented power to address these questions. To maximize the great potential these data we need the development of novel population genomic models and tools that address the increasing evidence for polygenic adaptation. In particular, while much attention has focused on understanding a simple model of the effect of adaptation, the full sweep model, the genome-wide effects of soft and partial sweeps has received almost no theoretical attention nor methods development. In addition while our understanding of the genetic basis of the variation in many human phenotypes has vastly improved through genome-wide association studies our understanding of how selection has shaped this highly polygenic variation across populations has lagged significantly. We propose a number of lines of research to address these significant shortcomings. Specifically to empower the study of the role of polygenic selection and adaptation in population genomic data we will: Aim 1) Develop an extended model of the population genomic effects of linked selection. We will construct new models of the effect of different modes of linked selection - including background selection, recurrent partial sweeps, and soft sweeps - on levels of genetic diversity, using cutting-edge coalescent methods. In Aim 2 we will develop the inference machinery to infer the genomic parameters of this extended model of linked selection. This will allow us to investigate the relative contribution of background selection, hard, and soft sweeps to genomic patterns of genetic diversity. Finally in aim 3 we will create tools to detect local adaptation on polygenic traits using data provided by genome-wide association studies. This method will test for the concerted signal of local adaptation on the genetic basis of particular phenotypes, while accounting for the confounding effects of drift and shared population history.